Structural Health Monitoring (SHM)

Working document

Author

Thyge Vinther Ludvigsen, s203591

Published

13 Feb, 2026

1 Research Question:

How can sensor placement in structural health monitoring of buildings be optimized by minimizing expected maintenance decision cost rather than maximizing damage detectability?

note: shift form physics optimal monitoring -> decision optimal monitoring.

Sub Questions:

  • How does sensor placement influence damage detection probability?
  • How do detection errors propagate into maintenance decisions? (what are the costs of false positives and false negatives?)
  • What is the economically optimal number and location of sensors?
  • What are the optimal number and type of non-vibration sensors to detect the effect of non-damage related effects (like temperature, humidity, etc.) on the vibration data?
  • When is SHM economically beneficial compared to periodic inspection?

more,

  • Can information be weighted by consequence of failure? (consequence of failure by loss of element)

Not focusing on:

  • Optimal Sensor data processing (onsite vs offsite)
  • Optimal sensor type (vibration vs non-vibration)

1.1 Problem Formulation

1.1.1 Events / categories:

  • \(S\) is the structural information (Stiffness, mass, geometry)
  • \(D \in \{D_0, D_1, D_2, ..., D_k\}\)
    • (D_0) = healthy
    • (D_i) = damage at location (e.g. stiffness reduction)
  • \(L\) is load and environmental conditions acting on the structure (temperature, humidity, wind, etc.)
  • \(x\) is an location on the structure
  • \(a \in \{\text{Do nothing},\ \text{Inspect},\ \text{Repair}\}\)

Sensor are placed at locations \(x\), where the product measurements is given as \(y\). \[ y = f(S, D, L, x) + \varepsilon \]

A damage detection algorithm estimates: \[ P(D_i | y) \]

Cost of decision \(a\) given damage state \(D_i\) is given as \(C(a, D_i)\).

Decision Healthy Damaged
Do nothing 0 Failure risk
Inspect Inspection cost Inspection cost
Repair Unnecessary repair Repair cost

note: this can be expanded to include false positives and false negatives, and the cost of these errors.

Expected decision cost: \[ \mathbb{E}[C | y] = \sum_{i} C(a, D_i) P(D_i | y) \]

1.1.2 Objective: Optimization Problem

chosen number and location of sensors \(x\) to minimize expected decision cost: \[ \boxed{ x^* = \arg\min_x \mathbb{E}[C_{total}(x)] } \]

where total cost includes:

\[ C_{total} = C_{sensors} + C_{false\ alarms} + C_{missed\ damage} + C_{inspection} \]

Expanded:

\[ \mathbb{E}[C_{total}] = C_{install}(x) \cdot P(FP|x)C_{FP} \cdot P(FN|x)C_{FN} \]

2 Focused Literature Review (week 2)

Objective: Extract methods, approaches and key insides form the literature

  • find 3 papers for each of the each topic.

What to focus on:

  • Methods and approaches
    • Input and output of the method
  • Mathematical representation
  • Assumptions
  • justification

Example of my ref:

Cawley (2018) PDF

2.1 General

2.2 Introduction of damage to the structure (D)

2.2.1 Paper 1

Rosafalco et al. (2021), PDF, (reading: skim)

  • there are 2 SHM main approaches:
    • “SHM model model-based”: the update of a numerical model (e.g. through Kalman flters or optimization) [1]
      • Have an hard time whit dealing whit the noise in the data
    • “SHM data-driven”: the use of data to directly estimate damage state (e.g. through machine learning) [2]
      • Supervised learning - ML, labelled data, damage state is known
      • Unsupervised learning - ML, unlabelled data, damage state is unknown
    • “Simulation-Based Classification (SBC)” - an hybrid approach, labeled data is created form FEM model [3]
      • need to take varying operational and environmental conditions into account (e.g. temperature, humidity, load, etc.)

2.3 Vibration-based SHM

note: this is both for model model-based and data-driven methods for damage detection.

2.3.1 Paper 1

Sun et al. (2023), PDF, (paper type: review, reading: detailed)

Local and global methods

note: Comments on strengths and weaknesses for each of the 5 methods are given (use them).

  • Vibration-based damage identification methods: [1]
    • natural frequency-based [section 2]
      • hard to distinguish between damage and environmental effects [3]
      • is an example “how to optimize the sampling interval to minimize the effects of measurement noise requires further research.” [4] and [section 2.2] (validates my research question)
    • mode shape-based [section 3] and modal curvature-based [section 3.2]
      • can be used to localize damage
      • ref to 2 papers where they try to use fever sensors to estimate the mode shapes [5]
      • ref to one paper where they down sampled the frequency whiteout losing mode shape [6]
      • sensitive to noise and environmental effects [7], [9]
      • large number of measurement points are needed to accurately estimate mode shapes [8]
      • many papers after [9]
    • Methods Based on Modal Strain Energy - combined methods based on both frequencies and mode shapes. [Section 4]
      • 2 stage model(in many cases): [10]
        • Damage is localized in the first stage by an damage index divided through strain energy, [10]
        • and then the severity of the damage is estimated in the second stage by an optimization optimization algorithms. [10]
        • (note there are references to may papers there cut be of relevance in the end of page 19)
      • Ref. to paper there uses PCA (Principal Component Analysis) - to uncouple collated variables like temperature and damage [11]
      • computationally expensive, for structures whit many elements [12]
      • If error in step 1 then can not be corrected in step 2 [13]
    • Methods Based on Modal Flexibility [section 5]
      • one study shows that the “Methods Based on Modal Flexibility” preform vers when many sensors are used, compared to “Methods curvature based method”, but it is not that sensitive to small damages? [14]
      • an real case study whit temperatures effects on stiffness [15]
      • they conclude that only the first couple of modes are needed to estimate the flexibility matrix and there for is there an need for fewer sensors [16]
      • they conclude that the flexibility based method is not good for damage severity [17]
    • machine learning / data-driven methods / statistical methods [2]
      • they are strong and can be used to filter out the noise and environmental effects, but if there is used supervised learning then there is a need for labeled data, which need much compute (note this is not based on this paper but is an general observation)

general methodology of vibration-based damage detection different Vibration based methods

2.4 Value-of-information-based optimal sensor placemen

2.4.1 Paper 1

Chadha et al. (2025), PDF, reading: detailed (but need more time to understand)

This paper holds allot of information about

  • VoI-based optimal sensor placement
  • Value based sensor placement
  • Economic properties
    • the cost of the sensors
    • the effect of the militance operators risk profiles
    • Some economic matrik close to opportunity cost (but not exactly)
    • ref 32 - is an paper for most of the economic model???
  • Appendix A, on page 28 has an Bayesian optimization algorithm for optimal sensor placement
    • notes they said it was fast, but do not find the optimal solution. (something whit using the sensors for last sensor configuration step????)

note: wiki miter gate monitoring

cost model: 32. Chadha M, Ramancha MK, Vega MA, et al. The modeling of risk perception in the use of structural health monitoring information for optimal maintenance decisions. Reliab Eng Syst Saf 2023; 229: 108845. (pdf) - Inflation rate, behavior of decision makers, Start cost, maintenance cost and operation cost, opportunity cost

The VoI metric over the structure’s lifecycle: expected utility theory (EUT)(pdf) - Expected utility hypothesis - it is an postulates that rational agents maximize utility.

nice summary of imploded methods: page 24 - (pdf)

  • suggestion to use VoI in conjunction whit information based optimal sensor placement to receive an robust system. “This leads us to recommend that VoI-based optimization should be used in conjunction with informationbased optimization. For instance, the first sensor can be optimized to maximize the VoI, while the subsequent additional sensors, conditioned on the first sensor, can be obtained by maximizing information gain.” (Chadha et al., 2025, p. 2116) (pdf)

Citations

Cawley, Peter. 2018. “Structural Health Monitoring: Closing the Gap Between Research and Industrial Deployment.” Structural Health Monitoring 17 (5): 1225–44. https://doi.org/10.1177/1475921717750047.
Chadha, Mayank, Zhen Hu, Charles R. Farrar, and Michael D. Todd. 2025. “A Value-of-Information-Based Optimal Sensor Placement Design Framework for Cost-Effective Structural Health Monitoring (with Application to Miter Gate Monitoring).” Structural Health Monitoring 24 (4): 2091–2124. https://doi.org/10.1177/14759217241275643.
Rosafalco, Luca, Matteo Torzoni, Andrea Manzoni, Stefano Mariani, and Alberto Corigliano. 2021. “Online Structural Health Monitoring by Model Order Reduction and Deep Learning Algorithms.” Computers & Structures 255 (October): 106604. https://doi.org/10.1016/j.compstruc.2021.106604.
Sun, Xutao, Sinniah Ilanko, Yusuke Mochida, and Rachael C. Tighe. 2023. “A Review on Vibration-Based Damage Detection Methods for Civil Structures.” Vibration 6 (4): 843–75. https://doi.org/10.3390/vibration6040051.